Avoiding unnecessary discretization in r2R0

[tamas-ferenci]

In parametric approach, serial interval is typically assumed to have Gamma distribution, so it would be perhaps useful to include a function

r2R0gamma <- function(r, si_mean, si_sd) {
  (1+r*si_sd^2/si_mean)^(mu^2/sigma^2)
}

in the package. Even the example of r2R0 is not really fortunate as it starts from mu and sigma being known, yet, it first transforms them to a discretized distribution, and then uses the empirical distribution formula from Wallinga and Lipitsch, which is obviously a convoluted approach, with a loss of precision.

As a comparison, r2R0 gives the values

[1]  0.0000000  0.9852657  1.0000000  1.0148667 98.7061545

for the example, while the true values according to my calculation are

[1]         NaN   0.9847737   1.0000000   1.0153739 168.8621648

[tamas-ferenci]

We could even have something like

r2R0parametric <- function(r, dist, ...) {
  if(!exists(paste0("mgf", dist), where = asNamespace("actuar")))
    stop(paste0("There is no moment generating function for ", dist, " in actuar package!"))
  1/do.call(get(paste0("mgf", dist), asNamespace("actuar")), list(t = -r, ...))
}